The lengths of the sides of a quadrilateral are 4 consecutive even integers. The perimeter of the quadrilateral is 36 inches. What is the length of the longest side?

12 inches

Step-by-step explanation:

Even integers are multiple of 2 and differ by 2.

Thus,

as quadrilaterals have 4 sides

let the length of those sides be

2x , 2x + 2 , 2x+4, 2x+6

given that their sum is 36 inches

thus

lets take sum of assumed sides

2x + 2x + 2 + 2x+4 +  2x+6 = 36

=> 8x + 12 = 36

=> 8x = 36 - 12 = 24

=> x = 24/8 = 3

Thus,

sides are

2x = 2*3 = 6

2x + 2 = 6 +2 = 8

2x + 4 = 6 + 4 = 10

2x + 6 = 6 + 6 = 12

Thus,

length of longest side is 12 inches.

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺